Lorentz 空间中超曲面上的 Ricci 孤立子
Ricci Solitons on Hypersurfaces of LorentzSpace
DOI: 10.12677/PM.2022.1212232, PDF, HTML, 下载: 260  浏览: 401  国家自然科学基金支持
作者: 杨 阳*, 杨 超#：西北师范大学数学与统计学院，甘肃 兰州
关键词: Ricci 孤立子；超曲面；Lorentz 空间；形状算子；主曲率；Ricci Solitons； Hypersurfaces； Lorentz Space； Shape Operator； Principal Curvatures
摘要: 本文研究 Lorentz 空间 E1n+1 中超曲面上以它的位置向量的切向为势向量场的 Ricci 孤立子。在超曲面的形状算子可对角化的假定下，得到超曲面至多有两个不相同的主曲率。
Abstract: In this paper, we study Ricci solitons on hypersurfaces of Lorentz space E1n+1 by taking the potential vector field as the tangent component of the position vector of the hypersurfaces. Under the assumption that the hypersurfaces have diagonalizable shape operators, we prove that the hypersurfaces have at most two distinct principal curvatures.
文章引用：杨阳, 杨超. Lorentz 空间中超曲面上的 Ricci 孤立子[J]. 理论数学, 2022, 12(12): 2163-2169. https://doi.org/10.12677/PM.2022.1212232

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